A straw is placed inside a rectangular box that is 2 inches by 6 inches by 8 inches, as shown. If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, how long is the straw? Leave your answer in the simplest radical form.

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

the circumference of a circle is, 10.676 cm.

step-by-step explanation:

the formula for circumference of a circle is given by:

where

c is the circumference of a circle and

d is the diameter of a circle.

given: diameter(d) = 3.4 cm and use

substitute these values in [1] we get;

cm

therefore, the circumference of a circle is, 10.676 cm